Mathematics
Grade10
Easy

Question

What are the equations of the asymptotes of the function f(x) = fraction numerator 1 over denominator left parenthesis straight x space minus space 5 right parenthesis end fraction + 3 ?

  1. Horizontal: y = 5 , Vertical : x = 3
  2. Horizontal: y = -3 , Vertical : x = 5
  3. Horizontal: x = 5 , Vertical : y = -3
  4. Horizontal: x = -3 , Vertical : y = 5

Hint:

In analytic geometry, an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the x or y coordinates tends to infinity. In projective geometry and related contexts, an asymptote of a curve is a line which is tangent to the curve at a point at infinity.

The correct answer is: Horizontal: y = -3 , Vertical : x = 5


    Here, we have to find the asymptotes to the graph y = 1/(x-5) +3.
    For the function, f(x) = fraction numerator straight a over denominator left parenthesis straight x space minus space straight h right parenthesis end fraction + k
    Horizontal asymptote: y = k
    Vertical asymptote: x = h
    In this case, asymptotes are x = 5 and y = -3.
    Hence, the correct option is B.

    Horizontal asymptote is y = k and vertical asymptote is x = h, where (h,k) is a moving point on the graph.

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